Due to an excessive amount of rain, the village water storage tank is filling at a rate of 600m (6+4t) litres a day (t≥ 0). The mayor is planning to evacuate the village before the water storage tank overflows, flooding the valley. The amount of water currently in the water storage tank is 17,894, 400 litres and the mayor wants to know how many days it will take for the water storage tank to be completely full. The water storage tank is a large cylinder which is 20 metres high and has a radius of 30 meters. You can assume that the villagers are not using any of the water storage water and there is no water loss through evaporation. (1) Give the volume of a cylinder. (2) What is the maximum capacity of the water storage tank in litres? (Hint: 1000 litres = 1 cubic metre) (3) Find the function that gives the number of litres in the water storage tank at time t days. (4) The village mayor wants to have the town evacuated before the water storage tank is full. At what time t would the water storage tank be full? (5) The mayor estimates that it will take 3 days to evacuate the village. When do you recommend that the evacuation begins and why?
Due to an excessive amount of rain, the village water storage tank is filling at a rate of 600m (6+4t) litres a day (t≥ 0). The mayor is planning to evacuate the village before the water storage tank overflows, flooding the valley. The amount of water currently in the water storage tank is 17,894, 400 litres and the mayor wants to know how many days it will take for the water storage tank to be completely full. The water storage tank is a large cylinder which is 20 metres high and has a radius of 30 meters. You can assume that the villagers are not using any of the water storage water and there is no water loss through evaporation. (1) Give the volume of a cylinder. (2) What is the maximum capacity of the water storage tank in litres? (Hint: 1000 litres = 1 cubic metre) (3) Find the function that gives the number of litres in the water storage tank at time t days. (4) The village mayor wants to have the town evacuated before the water storage tank is full. At what time t would the water storage tank be full? (5) The mayor estimates that it will take 3 days to evacuate the village. When do you recommend that the evacuation begins and why?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Due to an excessive amount of rain, the village water storage tank is filling at a rate
of 600m (6+4t) litres a day (t≥ 0). The mayor is planning to evacuate the village before
the water storage tank overflows, flooding the valley.
The amount of water currently in the water storage tank is 17,894, 400 litres and
the mayor wants to know how many days it will take for the water storage tank to be
completely full.
The water storage tank is a large cylinder which is 20 metres high and has a radius
of 30 meters.
You can assume that the villagers are not using any of the water storage water and
there is no water loss through evaporation.
(1) Give the volume of a cylinder.
(2) What is the maximum capacity of the water storage tank in litres? (Hint: 1000
litres = 1 cubic metre)
(3) Find the function that gives the number of litres in the water storage tank at
time t days.
(4) The village mayor wants to have the town evacuated before the water storage
tank is full. At what time t would the water storage tank be full?
(5) The mayor estimates that it will take 3 days to evacuate the village. When do
you recommend that the evacuation begins and why?
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